Lesson 24 3 5
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 24
Objective: Express whole numbers as fractions and recognize equivalence
with different units.
Suggested Lesson Structure
Fluency Practice

Application Problem

Concept Development

Student Debrief

Total Time
(12 minutes)
(5 minutes)
(33 minutes)
(10 minutes)
(60 minutes)
Fluency Practice (12 minutes)
 Sprint: Add by 7 2.NBT.5
(8 minutes)
 Write Equal Fractions 3.NF.3d
(4 minutes)
Sprint: Add by Seven (8 minutes)
Materials: (S) Add by Seven Sprint
Note: This Sprint supports fluency with addition by 7.
Write Equal Fractions (4 minutes)
Materials: (S) Personal white board
Note: This activity reviews the skill of finding equivalent fractions on the number line from Topic E.
T:
(Project number line with endpoints 0 and 1 partitioned into 2 equal parts by a dotted line.) Say the
unit fraction represented by the dotted line.
S:
1 half.
T:
(Write below the dotted line. To the right of the number line, write = .) On your personal
1
2
1
2
4
white board, write the number sentence, and fill in the blank.
S:
T:
1
2
2
(Write 4
2
4
(Write = .)
1
below 2 on the number line.)
Continue with the following possible sequence, drawing a new number line for each example:
1
4
1
3
=
2
and
= 8.
Lesson 24:
Express whole numbers as fractions and recognize equivalence with
different units.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G3-M5-TE-1.3.0-06.2015
275
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 24 3 5
NYS COMMON CORE MATHEMATICS CURRICULUM
Application Problem (5 minutes)
8
The zipper on Robert’s jacket is 1 foot long. It breaks on the first day of winter. He can only zip it 12 of the
way before it gets stuck. Draw and label a number line to show how far Robert can zip his jacket.
a. Divide and label the number line in thirds. What fraction of the way can he zip his jacket in thirds?
b. What fraction of Robert’s jacket is not zipped? Write your answer in twelfths and thirds.
NOTES ON
MULTIPLE MEANS
OF ENGAGEMENT:
Partitioning the interval into two
different fractional units is a
stimulating challenge for students
working above grade level.
Students working below grade level can
draw two separate number lines or use
fraction strips to solve.
Note: This problem reviews the skill of finding equivalent fractions on the number line from Topic E. Invite
students to share their strategies for partitioning the number line into thirds and twelfths.
Concept Development (33 minutes)
Materials: (S) Fraction pieces (Template), scissors, envelope,
personal white board, sentence strip, crayons
Each student starts with the fraction pieces, an envelope, and
scissors.
T:
S:
T:
S:
Cut out all of the rectangles on the fraction pieces, and
initial each rectangle so you know which ones are yours.
(Cut and initial.)
Place the rectangle that says 1 whole on your personal
white board. Take another rectangle. How many halves
make 1 whole? Show by folding and labeling each unit
fraction.
1 whole
halves
thirds
fourths
sixths
1
(Fold the second rectangle in half, and label 2 on each of the 2 parts.)
Lesson 24:
Express whole numbers as fractions and recognize equivalence with
different units.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G3-M5-TE-1.3.0-06.2015
276
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 24 3 5
NYS COMMON CORE MATHEMATICS CURRICULUM
T:
S:
T:
Now, cut on the fold. Draw circles around your whole and
your parts to make a number bond.
(Draw a number bond using the shapes to represent
wholes and parts.)
In your whole, write an equality that shows how many
halves are equal to 1 whole. Remember, the equal sign is
like a balance. Both sides have the same value.
2
=2
S:
(Write 1 whole
in the 1 whole rectangle.)
T:
Put your halves inside your envelope.
1 whole
1
2
1
2
Follow the same sequence for each rectangle so that students cut all pieces indicated. Have students update
the equality on their 1 whole rectangle each time they cut a new piece. At the end, it should read: 1 whole =
2
3
4
6
= 3 = 4 = 6. Discuss the equality with students to ensure that they understand the meaning of the equal
2
sign and the role it plays in this number sentence.
Project or show Image 1, shown to the right.
T: Use your pieces to make this number bond on your
board.
S: (Make the number bond.)
T: Discuss with your partner: Is this number bond true?
Why or why not?
S: No, because the whole has only 2 pieces, but there are
4 parts!  But fourths are just halves cut in 2. So,
2
they’re the same pieces, but smaller now.  4 is
1
2
T:
S:
2
2
4
and 4
I hear some of you saying that
both equal
1 whole. So, can we say that this is true? (Project or
show Image 2, shown on the next page.)
No, because thirds aren’t halves cut in 2. They look
completely different.  But, when we put our thirds
together and halves together, they make the same
whole.  Before, we found with our pieces that 1
2
3
4
whole = 2 = 3 = 4.  Then, it must be true!
Lesson 24:
1
2
1
4
1
4
1
2
1
4
1
4
4
equivalent to 2.  So, 2 = 4, just like what we wrote
down on our 1 whole rectangle.
MP.7
Image 1
NOTES ON
MULTIPLE MEANS
OF ENGAGEMENT:
Students working below grade level
may appreciate tangibly proving that
2 halves is the same as 4 fourths.
Encourage students to place the
(paper) fourths on top of the halves to
show equivalency.
Express whole numbers as fractions and recognize equivalence with
different units.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G3-M5-TE-1.3.0-06.2015
277
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 24 3 5
NYS COMMON CORE MATHEMATICS CURRICULUM
Follow the same sequence with a variety of wholes and parts until
students are comfortable with this representation of equivalence.
T:
S:
T:
S:
T:
S:
T:
S:
T:
S:
Image 2
Now, let’s place our different units on the same number
1
1
line. Use your sentence strip to represent the interval from
2
2
0 to 1 on a number line. Mark the endpoints with your
pencil now.
1
(Mark endpoints 0 and 1 below the number line.)
3
1
Go ahead and fold your sentence strip to partition one unit
3
1
at a time into halves, fourths, thirds, and then sixths. Label
3
each fraction above the number line. As you count, be sure
to rename 0 and the whole. Use a different color crayon to
mark and label the fraction for each unit.
(Fold the sentence strip and first label halves, then fourths, then thirds, and then sixths in different
colors. Rename 0 and 1 in terms of each new unit.)
You should have a crowded number line! Compare it to your partner’s.
(Compare.)
Before today, we’ve been noticing a lot of equivalent fractions between wholes on the number line.
Today, notice the fractions you wrote at 0 and 1. Look first at the fractions for 0. What pattern do
you notice?
They all have 0 copies of the unit!  The total number of equal parts changes. It shows you what
unit you’re going to count by.  Since our number line starts at 0, there is 0 of that unit in all of the
fractions.
Even though the unit is different in each of our
fractions at 0, are they equivalent? Think back to
our work with shapes earlier.
We saw before that fractions with different units
can still make the same whole. This time, the
whole is just 0.
Follow the sequence to study the fractions written at 1.
For both 0 and 1, students should see that every color
they used is present.
Problem Set (10 minutes)
Students should do their personal best to complete the
Problem Set within the allotted 10 minutes. For some
classes, it may be appropriate to modify the assignment by
specifying which problems they work on first. Some
problems do not specify a method for solving. Students
should solve these problems using the RDW approach
used for Application Problems.
Lesson 24:
Express whole numbers as fractions and recognize equivalence with
different units.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G3-M5-TE-1.3.0-06.2015
278
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 24 3 5
NYS COMMON CORE MATHEMATICS CURRICULUM
Student Debrief (10 minutes)
Lesson Objective: Express whole numbers as fractions
and recognize equivalence with different units.
The Student Debrief is intended to invite reflection and
active processing of the total lesson experience.
Invite students to review their solutions for the Problem
Set. They should check work by comparing answers with a
partner before going over answers as a class. Look for
misconceptions or misunderstandings that can be
addressed in the Student Debrief. Guide students in a
conversation to debrief the Problem Set and process the
lesson.
Any combination of the questions below may be used to
lead the discussion.




Invite students to share their thinking about
Problem 3.
Invite students to share their work on Problem 4.
Have students use their fraction shapes from the
lesson to model the number bonds in Problem 1.
Ask students to generate other fractions equivalent to 1 whole. Provide the unit, and ask them to
generate the fraction. The following is an example:
T: The unit is millionths. What fraction is equivalent to 1 whole?
S: Wow! 1,000,000 millionths!
Exit Ticket (3 minutes)
After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help with
assessing students’ understanding of the concepts that were presented in today’s lesson and planning more
effectively for future lessons. The questions may be read aloud to the students.
Lesson 24:
Express whole numbers as fractions and recognize equivalence with
different units.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G3-M5-TE-1.3.0-06.2015
279
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 24 Sprint 3 5
NYS COMMON CORE MATHEMATICS CURRICULUM
Number Correct:
A
Add by Seven
1.
0+7=
23.
6+7=
2.
1+7=
24.
16 + 7 =
3.
2+7=
25.
26 + 7 =
4.
3+7=
26.
36 + 7 =
5.
7+3=
27.
46 + 7 =
6.
7+2=
28.
66 + 7 =
7.
7+1=
29.
7+7=
8.
7+0=
30.
17 + 7 =
9.
4+7=
31.
27 + 7 =
10.
14 + 7 =
32.
37 + 7 =
11.
24 + 7 =
33.
87 + 7 =
12.
34 + 7 =
34.
8+7=
13.
44 + 7 =
35.
18 + 7 =
14.
84 + 7 =
36.
28 + 7 =
15.
64 + 7 =
37.
38 + 7 =
16.
5+7=
38.
78 + 7 =
17.
15 + 7 =
39.
9+7=
18.
25 + 7 =
40.
19 + 7 =
19.
35 + 7 =
41.
29 + 7 =
20.
45 + 7 =
42.
39 + 7 =
21.
75 + 7 =
43.
49 + 7 =
22.
55 + 7 =
44.
79 + 7 =
Lesson 24:
Express whole numbers as fractions and recognize equivalence with
different units.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G3-M5-TE-1.3.0-06.2015
280
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 24 Sprint 3 5
NYS COMMON CORE MATHEMATICS CURRICULUM
Number Correct:
B
Improvement:
Add by Seven
1.
7+0=
23.
6+7=
2.
[KEY]
7+1=
24.
16 + 7 =
3.
7+2=
25.
26 + 7 =
4.
7+3=
26.
36 + 7 =
5.
3+7=
27.
46 + 7 =
6.
2+7=
28.
76 + 7 =
7.
1+7=
29.
7+7=
8.
0+7=
30.
17 + 7 =
9.
4+7=
31.
27 + 7 =
10.
14 + 7 =
32.
37 + 7 =
11.
24 + 7 =
33.
67 + 7 =
12.
34 + 7 =
34.
8+7=
13.
44 + 7 =
35.
18 + 7 =
14.
74 + 7 =
36.
28 + 7 =
15.
54 + 7 =
37.
38 + 7 =
16.
5+7=
38.
88 + 7 =
17.
15 + 7 =
39.
9+7=
18.
25 + 7 =
40.
19 + 7 =
19.
35 + 7 =
41.
29 + 7 =
20.
45 + 7 =
42.
39 + 7 =
21.
85 + 7 =
43.
49 + 7 =
22.
65 + 7 =
44.
89 + 7 =
Lesson 24:
Express whole numbers as fractions and recognize equivalence with
different units.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G3-M5-TE-1.3.0-06.2015
281
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 24 Problem Set 3 5
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
Date
1. Complete the number bond as indicated by the fractional unit. Partition the number line into the given
fractional unit, and label the fractions. Rename 0 and 1 as fractions of the given unit. The first one is
done for you.
Halves
Thirds
1
0
1
0
1
0
1
0
1
1
Fourths
1
Fifths
1
Lesson 24:
Express whole numbers as fractions and recognize equivalence with
different units.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G3-M5-TE-1.3.0-06.2015
282
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 24 Problem Set 3 5
2. Circle all the fractions in Problem 1 that are equal to 1. Write them in a number sentence below.
2
2
= _______________ = __________________ = ___________________
3. What pattern do you notice in the fractions that are equivalent to 1?
4. Taylor took his little brother to get pizza. Each boy ordered a small pizza. Taylor’s pizza was cut in
fourths, and his brother’s was cut in thirds. After they had both eaten all of their pizza, Taylor’s little
brother said, “Hey that was no fair! You got more than me! You got 4 pieces, and I only got 3.”
Should Taylor’s little brother be mad? What could you say to explain the situation to him? Use words,
pictures, or a number line.
Lesson 24:
Express whole numbers as fractions and recognize equivalence with
different units.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G3-M5-TE-1.3.0-06.2015
283
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
Lesson 24 Exit Ticket 3 5
Date
1. Complete the number bond as indicated by the fractional unit. Partition the number line into the given
fractional unit, and label the fractions. Rename 0 and 1 as fractions of the given unit.
Fourths
1
0
1
1
2. How many copies of does it take to make 1 whole? What’s the fraction for 1 whole in this case? Use
4
the number line or the number bond in Problem 1 to help you explain.
Lesson 24:
Express whole numbers as fractions and recognize equivalence with
different units.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G3-M5-TE-1.3.0-06.2015
284
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
Lesson 24 Homework 3 5
Date
1. Complete the number bond as indicated by the fractional unit. Partition the number line into the given
fractional unit, and label the fractions. Rename 0 and 1 as fractions of the given unit.
Fifths
1
0
1
Sixths
1
0
1
0
1
0
1
Sevenths
1
Eighths
1
Lesson 24:
Express whole numbers as fractions and recognize equivalence with
different units.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G3-M5-TE-1.3.0-06.2015
285
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 24 Homework 3 5
2. Circle all the fractions in Problem 1 that are equal to 1. Write them in a number sentence below.
5
5
= _______________ = __________________ = ___________________
3. What pattern do you notice in the fractions that are equivalent to 1? Following this pattern, how would
you represent ninths as 1 whole?
4. In Art class, Mr. Joselyn gave everyone a 1-foot stick to measure and cut. Vivian measured and cut her
stick into 5 equal pieces. Scott measured and cut his into 7 equal pieces. Scott said to Vivian, “The total
length of my stick is longer than yours because I have 7 pieces, and you only have 5.” Is Scott correct?
Use words, pictures, or a number line to help you explain.
Lesson 24:
Express whole numbers as fractions and recognize equivalence with
different units.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G3-M5-TE-1.3.0-06.2015
286
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 24 Template 3 5
NYS COMMON CORE MATHEMATICS CURRICULUM
sixths
Pieces

thirds
1 whole
halves
fourths

fraction pieces
Lesson 24:
Express whole numbers as fractions and recognize equivalence with
different units.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G3-M5-TE-1.3.0-06.2015
287
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.